What are the Different Types of Triangles

Classification of Triangles

A triangle is a polygon with three sides. It has three sides and three vertices. There are seven types of triangles. The sum of the angles of a triangle is 180°.

Triangles Types can be classified in two ways:

  1. By their sides
  2. By their angles

what are the six types of triangles?

Six Various Types of Triangles are Isosceles, Equilateral, Obtuse, Acute and Scalene.

Classification of Triangles by Sides

Scalene Triangle:
A triangle that has no side of equal length is called a scalene triangle.
What are the Different Types of Triangles 1In figure, PQ ≠ QR ≠ PR, so ΔPQR is a scalene triangle.

Isosceles Triangle:
A triangle that has two sides of equal length, is called an isosceles triangle.
What are the Different Types of Triangles 2In figure, AB = AC, so ΔABC is an isosceles triangle.

Equilateral Triangle:
A triangle which has all the three sides equal in length is called an equilateral triangle.
What are the Different Types of Triangles 3In figure, PQ = QR = PR, so ΔPQR is an equilateral triangle.

Classification of Triangles by Angles

Acute-angled Triangle:
A triangle whose all angles are acute (less than 90°), is called an acute-angled triangle or simply an acute triangle.
What are the Different Types of Triangles 4In figure, ∠A, ∠B, and ∠C are all less than 90°, hence ΔABC is an acute-angled triangle.

Right-angled Triangle:
A triangle whose one of the angles is a right angle, i.e., 90°, is called a right-angled triangle or simply right triangle.
What are the Different Types of Triangles 6In figure, ∠B = 90°, hence ΔABC is a right triangle.

Obtuse-angled Triangle:
A triangle whose one angle is obtuse, is called an obtuse-angled triangle or simply obtuse triangle.
What are the Different Types of Triangles 5In figure, ∠Y is obtuse, hence ΔXYZ is an obtuse-angled triangle or simply obtuse triangle.

Equiangular Triangle:
When all the three angles of a triangle are equal, then it is known as an equiangular triangle.
An equiangular triangle is also known as equilateral triangle because all the three sides are equal.
What are the Different Types of Triangles 7In figure, ∠A = ∠B = ∠C = 60°and AB = BC = AC, hence ΔABC is an equiangular triangle.

Example 1: One of the equal angles of an isosceles triangle is 50°. Find its third angle.
Solution: Let third angle = x
∴ x + 50° + 50° = 180°
(Angle sum property of a triangle)
or,   x + 100° = 180°
or,   x = 180° – 100°
= 80°
∴ Third angle = 80°

Example 2: Each ofthe two equal angles of a triangle is four times the third angle. Find all the angles of the triangle.
Solution: Let the smaller angle = x
∴ other two angles = 4x and 4x
Thus, x + 4x + 4x = 180°
(Angle sum property of a triangle) or, 9x = 180°
∴ 4x = 4 x 20°
= 80°
Thus, the angles of the triangle are 20°, 80°, and 80°.

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